Patriots tight end Matthew Mulligan has done pretty well for himself for a kid who was an undrafted free agent out of Maine.

He’s now in his sixth NFL season, and has played in 52 career games with 20 starts. He even caught a touchdown pass last year with the Rams — a nice little reward for a blocking tight end who mostly plays special teams.

But Mulligan put his ego aside after the Packers cut him last month at the end of training camp. When the Patriots and then the Ravens called in early September to see if he would try out, he was on the first plane to New England, and then Baltimore.

“You go from the last few years starting 18 games, playing a ton of snaps, and then going back down and basically working your way up again,” said Mulligan, who signed with the Patriots Sept. 3, just hours after his tryout. “But the bottom line is it’s a blessing to be at least able to have a tryout. I’m not going to let my pride get in the way of being able to extend my career in the NFL.”

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NFL pro personnel departments do most of their roster building in the offseason, but they stay busy during the fall by holding tryouts and hosting players on official visits, often on Tuesdays and Fridays, the slowest work days of the week. And the Patriots have been especially busy this season compared with their counterparts.

The Globe obtained every NFL personnel notice since the start of the regular season, and the Patriots had worked out 29 players through Tuesday, tied with the Giants for most in the NFL. The league average is 10 tryouts per team, and New Orleans and Jacksonville had yet to hold one as of Tuesday.

Patriots coach Bill Belichick said he has several reasons for trying out a player. In Mulligan’s case, the Patriots badly needed a tight end after keeping just two healthy ones at the end of camp (Michael Hoomanawanui and Zach Sudfeld). Sometimes they are looking to improve the bottom of the roster or the practice squad, sometimes they want to see how a player has come back from an injury, and in other cases, they are simply looking at guys to compile an “in case of emergency” list if one of their key players suffers an injury later in the season.

“Just trying to stay on top of the guys that we feel like we need to look at, whether that’s guys we don’t know or guys that might have been involved in an injury situation,” Belichick said. “Some guys, if they have an injury situation, we just want to see where they are — whether we should have them on any list at all, or maybe that’s a guy we want to bring back in October and November.”

On Sept. 6, the Patriots worked out 11 players — quarterbacks, wide receivers, running backs, and nose tackles. Some were little-known rookies looking for a shot, and some were familiar names, such as quarterback Graham Harrell and running back Jonathan Dwyer. Three days later, they tried out 12-year defensive end Andre Carter, who had 10 sacks for the Patriots in 2011.

Overall, the Patriots have tried out: 3 QBs, 4 RBs, 3 WRs, 3 TEs, 4 DEs, 3 DTs, 7 LBs, and 2 DBs. The other two quarterbacks were rookie B.J. Coleman from Tennessee-Chattanooga and rookie Austin Davis from Southern Mississippi. Of the 29, only Mulligan came away with a contract. He was cut two days later on Sept. 5, tried out for the Ravens four days after that, and was signed by the Patriots again that night.

He has played in two of the Patriots’ three games, totaling 19 offensive snaps and five on special teams. Mulligan said his Patriots tryout only lasted about 20 minutes. He was the only player involved, and was observed by members of the pro personnel department, led by Nick Caserio and Bob Quinn, the director of pro scouting. Since Mulligan is a proven blocker on the NFL level, the workout mostly involved him running routes and catching passes. Caserio served as the quarterback.

“I didn’t know who he was at first, but he threw a good ball,” said Mulligan, 28. “There’s quite a bit of pressure there. You can feel it, because all eyes are on you.”

Belichick, who attends some but not all of the tryouts, said players better be able to handle the pressure, because life doesn’t get any easier on NFL Sundays. “I plan on being at all the games,” he quipped, “so if they can’t perform with me there, then it’s probably not going to work.”

Mulligan is lucky that he signed fairly quickly each time after being released this season. Some players get caught up in the “tryout circuit,” bouncing around the country trying to find a team that needs their services.

Just this month, ex-Eagles linebacker Jamar Chaney tried out with the Lions, Titans, and Patriots before trying out for and signing with the Falcons Sept. 17. Former Giants first-round defensive tackle Marvin Austin tried out for the Lions, Seahawks, Chiefs, and Bengals before trying out for and signing with the Dolphins last week.

Mulligan, from Enfield, Maine, has bounced around the country in his six seasons, playing for the Dolphins, Titans, Jets, Packers, and Patriots. He said he has developed a mercenary mentality in order to prolong his career.

“I’ll play for anybody who wants me. I’m loyal to the team that I’m with, and obviously now I’m loyal to the Patriots,” said Mulligan. “It kind of feels like my rookie year, because you’re day to day, essentially. It’s tough, but as long as you’re still here, it’s a blessing.”

WHAT’S THE DEAL?

Some money matters concerning Patriots

■ The Patriots got a pretty good deal on the three-year contract extension for defensive end Rob Ninkovich, one of their more consistent and productive players. The trade-off for Ninkovich is he gets some good money now, and roster security for one or two more years.

Ninkovich realistically signed an extension worth $7 million guaranteed through 2015, receiving a $5 million signing bonus and $1 million in base salary guaranteed in 2014 and 2015. And that last $1 million in 2015 only becomes guaranteed if he is still on the roster on the fifth day of the league year.

Ninkovich has $200,000 bonuses for making the Pro Bowl, and each year starting in 2014 will make $15,625 each game he is on the active roster, up to $250,000. His salary-cap number will only jump by about $600,000 this year, to $3.62 million. His final three cap numbers are $2.7 million, $3.7 million, and $3.15 million.

■ One person who doesn’t mind if Rob Gronkowski takes his time coming back is tight end Michael Hoomanawanui. His renegotiated contract pays him an extra $125,000 if he plays in 25 percent of snaps for the season, $250,000 if he plays 35 percent, and $370,000 if he plays 45 percent. With Gronkowski and then Zach Sudfeld hurt this year, Hoomanawanui has played in 186 of 230 snaps (81 percent). He might have to get the bulk of his snaps in early in the season, although he should continue to have a role as a blocking tight end and H-back throughout.

Speaking of snap counts, left guard Logan Mankins, center Ryan Wendell, and quarterback Tom Brady are the only offensive players who have played 100 percent of the snaps on offense. Julian Edelman leads all skill players with 210 snaps (91 percent), followed by rookie Kenbrell Thompkins at 208 (90 percent).

On defense, safety Devin McCourty and cornerback Aqib Talib are the only players to play all 203 snaps, followed by ends Chandler Jones (198) and Ninkovich (195).

NOT ALL BAD

Buccaneers’ Freeman still has some value

Amid the Josh Freeman bash-fest last week, when the Buccaneers’ 2009 first-round pick was finally removed from the starting quarterback job after one-plus inconsistent seasons with coach Greg Schiano, his agent had a message:

And this isn’t just agent bluster. Freeman, still only 25, does have some impressive bullet points on his résumé. He threw 25 TD passes against just six interceptions in 2010 while leading the Buccaneers to a 10-6 record, and last year cracked 4,000 yards for the first time. He’s also 6 feet 6 inches and mobile.

The rift between Freeman and Schiano was one of the worst-kept secrets in the NFL, and Freeman wants out of Tampa Bay sooner rather than later. But he may have to be patient.

Teams needing a new quarterback tend to fill that hole in the draft, hoping to strike it big on a first-round rookie. It’s likely that Freeman’s only chance of getting traded out of Tampa Bay before the Oct. 29 deadline would come if a playoff-contending team loses its quarterback to injury.

Outside of that, he’ll have to wait until hitting free agency next spring. While he will have plenty of offers to serve as a backup and possibly push an incumbent for a starting job, Freeman is facing an uphill battle to reclaim a starting spot in the NFL.

ETC.

Dolphins are keeping fast start in perspective

Publicly, the Dolphins have been talking big in 2013, with the team using an official motto of “It’s Our Time” after spending more than $98 million guaranteed in free agency this offseason. And the Dolphins have been one of the NFL’s biggest surprises, taking a 3-0 record into their Monday night showdown at 3-0 New Orleans, with impressive wins over Indianapolis and Atlanta in the past two weeks.

But the front office isn’t bragging or boasting or thinking too much about getting back to the playoffs for the first time since 2008. The Dolphins, of course, remember the 2010 team that started 2-0 and finished 7-9. And they have seen teams like the 2012 Bears, who began 7-1 and missed the playoffs.

Cautious optimism would be a good way to put it. I sent a text to one front office source last Sunday, congratulating his team on a last-second win over Atlanta.

The reply? “One week at a time.”

I texted another source that second-year quarterback Ryan Tannehill looked great last week in leading the Dolphins to a game-winning touchdown.

“When it counted. When it counted,” was the answer back.

Cold starts in Florida

Staying down in Florida, the other two teams are the polar opposite of Miami — the Buccaneers and Jaguars are both off to 0-3 starts, and their owners already are having trouble filling seats.

The Buccaneers, who have had 19 of their last 24 home games blacked out in the Tampa Bay market after failing to sell out Raymond James Stadium, announced Wednesday that the team’s remaining home games will be shown on local TV as a way to keep fans interested.

Ownership will have to purchase enough tickets each week for the team to reach the 85 percent threshold in order for games to avoid blackouts, although NFL rules allow teams to purchase their own seats at 34 percent of face value.

The Jaguars, meanwhile, are reverting to more desperate measures. The Jaguars have actually done fairly well in attendance the last few years — they ranked 17th in the NFL by selling 96.8 percent of their seats last year, one spot ahead of the Packers — but they have scored just 28 points in three games and interest in North Florida is waning fast.

So, how are the Jaguars getting fans in the seats for Sunday’s game against the Colts? The oldest trick in the book — free beer.

At 10 a.m. Thursday, the Jaguars announced that any ticket purchase (minimum $45) would be accompanied by two free Bud Lights at the game.

They’re headed down a slippery slope — the last thing the NFL wants is for a fan to be overserved and then hit the road after the game — but the Jaguars have realized the easiest and most cost-effective way to bring fans back to the seats.

Not with a fancy Jumbotron or live locker room video or a fantasy football lounge. Just make the beer cheaper.

Messy business

Roger Goodell has another legal issue with an ownership group on his hands — the second time this year one of his owners is embroiled in a fraud scandal.

First it was Browns owner Jimmy Haslam and his truck stop company, Pilot Flying J, caught up in a rebate scam. Now Vikings owners Zygi and Mark Wilf have been ordered by a New Jersey court to pay $84.5 million in damages for “organized crime-type activities,” as Superior Court Judge Deanna Wilson put it, in scamming their former business partners out of profits in an apartment complex. The Wilfs plan to appeal, and the matter could last several more years.

“The bad faith and evil motive were demonstrated in the testimony of Zygi Wilf himself,” Wilson said. “It was not even grossly negligent. It was grossly willful. And it was done repeatedly.”

Not only is this another bad look for Goodell and the NFL, but the Vikings got a new stadium deal this year in which the Wilf family is responsible for paying $477 million of the $975 million cost. The downtown Minneapolis stadium is supposed to be ready for the 2016 season, and Peter Harvey, the Wilfs’ attorney, said “nothing that the judge has decided will impact stadium construction.”

Extra points

Saints quarterback Drew Brees can tie his own record Monday night against the Dolphins. He has recorded eight straight 300-yard passing games, and the record is nine, which he set between 2011 and 2012. Steve Young, Kurt Warner, and Rich Gannon are next on the list with six straight 300-yard games . . . There were 101 sacks last weekend, the second most in a week in NFL history (102 in Week 11, 1986). Kansas City linebacker Justin Houston did his part with 4½ . . . The referee for Sunday night’s Patriots-Falcons game: Walt Coleman, i.e. the guy who introduced the nation to the “Tuck Rule.” . . . Don’t look now, but the Broncos have won 14 straight regular-season games, with their last loss coming in Week 5 last year at New England. Their upcoming schedule doesn’t seem too daunting — vs. Philadelphia Sunday, at Dallas, vs. Jacksonville, at Indianapolis, vs. Washington, bye, at San Diego, and vs. Kansas City. The NFL record is 23 straight regular-season victories by the 2008-09 Colts (the 2003-04 Patriots hold the longest true winning streak at 21 regular-season and playoff games). The common thread between this year’s Broncos and those Colts teams, of course: some guy named Peyton Manning.

Ben Volin can be reached at ben.volin@globe.com. Follow him on Twitter @BenVolin. Material from interviews, wire services, other beat writers, and league and team sources was used in this report.